A124668 Numbers that together with their prime factors contain every digit exactly once.

10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584

Offset

1,1

Comments

The exponents in the prime factorization are not considered here. See A273260 for that variant, which contains, e.g., 26487 = 3^5 * 109 and 61054 = 2 * 7^3 * 89. - M. F. Hasler, May 28 2024

Links

Table of n, a(n) for n=1..8.

Example

10968 = 2^3 * 3 * 457.

Maple

isA124668 := proc(n) local digs, digs2, f, fac, b ; digs := convert(n, base, 10) ; f := ifactors(n)[2] ; for fac from 1 to nops(f) do b := op(1, op(fac, f)) ; digs := [op(digs), op(convert(b, base, 10))] ; od ; digs2 := convert(digs, set) ; if nops(digs2) = 10 and nops(digs2)=nops(digs) then print(n, f) ; RETURN(true) ; else RETURN(false) ; fi ; end : A124668aux := proc(n, dleft) local i, nnxt, dnxt ; isA124668(n) : for i from 1 to nops(dleft) do nnxt := 10*n+op(i, dleft) ; dnxt := dleft minus {op(i, dleft)} ; if nops(dnxt) > 0 then A124668aux(nnxt, dnxt) ; fi ; od ; end : dleft := {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} : for i from 1 to 9 do dnxt := dleft minus {i} ; A124668aux(i, dnxt) : od : # R. J. Mathar, Jan 13 2007

Mathematica

Select[Range[2, 1000000], Sort[Join[IntegerDigits[ # ], Flatten[IntegerDigits[Transpose[FactorInteger[ # ]][[1]]]]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]

Prog

(PARI) is_A124668(n) = { vecsum([logint(f, 10)+1 | f<-n=concat(factor(n)[, 1], n)])==10 && #Set(concat([digits(f) | f<-n]))>9 }
L=List(); forvec(v=vector(5, i, [0, 9]), forperm(v, n, is_A124668(n=fromdigits(Vec(n)))&& listput(L, n)), 2); A124668=Set(L) \\ M. F. Hasler, Jun 05 2024

Crossrefs

Cf. A273260: similar, but digits of exponents > 1 in the prime factorization are also taken into account.

Sequence in context: A205052 A251170 A035913 * A270148 A270115 A335082

Adjacent sequences: A124665 A124666 A124667 * A124669 A124670 A124671

Keyword

base,fini,full,nonn

Author

Tanya Khovanova, Dec 23 2006

Status

approved